Some security bounds for the key sizes of DGHV scheme

Abstract

The correctness in decrypting a ciphertext after some operations in the DGVH scheme depends heavily on the dimension of the secret key. In this paper we compute two bounds on the size of the secret key for the DGHV scheme to decrypt correctly a ciphertext after a fixed number of additions and a fixed number of multiplication. Moreover we improve the original bound on the dimension of the secret key for a general circuit.